1 . 在三棱锥
中,
,平面
平面ABC,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/22/24b554a3-f871-428d-9d93-7172b0969ec4.png?resizew=147)
(1)证明:
平面
;
(2)棱BC上是否存在点D,使得面
与面
的夹角为
?若存在,求BD长度;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db99494753dbb4588ded0394a9e18607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376c005548874df605a76a086a82c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9b8e7befcb7881c294070175b1a554.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/22/24b554a3-f871-428d-9d93-7172b0969ec4.png?resizew=147)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da035673ef0edcfae6b72fb5e5ba34a.png)
(2)棱BC上是否存在点D,使得面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d39f37441ee55dbc8f1a6ca199a66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3520ee9cc97a075e889e1625dba1157c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8ae071199874d9d74a4919a58902f7.png)
您最近一年使用:0次
名校
2 . 如图,在三棱锥中,
,其余各棱的长均为6,点
在棱
上,
,过点
的平面与直线
垂直,且与
,
分别交于点
,
.
(1)确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
2024-03-27更新
|
621次组卷
|
2卷引用:老华大联盟2024届高三下学期3月联考理科数学试卷(全国乙卷)
3 . 在三棱柱
中,
,在底面
中,有
,且
,点
为等腰三角形
的底边
的中点,在
中,有
.
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a409e9c082608b0bc0baa4eb06e9a0eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83ac3df19eb9681acc5e981e429f647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239198e40085b7dcffbe747c9c265a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd247ebbe6abf3961c0e45dda866896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09659b96a28eac447408ac2b599a3e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/12c15294-3d6a-4ec1-a33b-28b211eacbd9.png?resizew=112)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80803823c1d79b719e7f0155f82a1876.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8358b9bfd17eb4cb819a4d652b6b561.png)
您最近一年使用:0次
解题方法
4 . 如图,在
中,
,在直角梯形
中,
,
,记二面角
的大小为
,若
,则直线
与平面
所成角的正弦值的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c542f78c489a714f0c02355c64e994c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8fac2c3290c9e57f4c0cf90fd5797c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dafb1a0ad813ac32b1d3f9c408f623d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327d8da21304d2763e18db07fe65b4f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d08f4d454ce6cb511668f40181e526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b73845874fe5e54679d99f9fd5e3b54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5610dc0acc42d3c5e5c60847842f7254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e6629d0e1a4ce3fe4f0345f6961473.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/d4733e89-14fa-4b99-bfc7-f64283780598.png?resizew=137)
您最近一年使用:0次
2024-02-21更新
|
1097次组卷
|
3卷引用:福建省名校联盟全国优质校2024届高三大联考数学试卷
福建省名校联盟全国优质校2024届高三大联考数学试卷(已下线)专题02 求空间角及空间向量的应用(三大类型)云南省大理州祥云县部分高中(云·上联盟五校协作体)2024届高三下学期复习摸底诊断联合测评数学试题
名校
5 . 如图所示,已知
是以
为斜边的等腰直角三角形,点
是边
的中点,点
在边
上,且
.以
为折痕将
折起,使点
到达点
的位置,且平面
平面
,连接
.
是线段
的中点,求证:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2f5ccf0f933aa0d48d237f8f9d29af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d0469336f71edd52dc9148c67db052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5618714583a99a7d6277349314851e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12c314dc346e29f4ab1e8c620ee4be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c83b7a6607eb72244afdd6a3cb020f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8010e1a73f05117a278860c1c0c7f147.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
您最近一年使用:0次
2024-01-16更新
|
598次组卷
|
3卷引用:THUSSAT2023-2024学年高三上学期1月诊断性测试数学试题
THUSSAT2023-2024学年高三上学期1月诊断性测试数学试题(已下线)第四章 立体几何解题通法 专题一 降维法 微点3 降维法(三)【基础版】浙江省嘉兴市第一中学2024届高三第一次模拟测试数学试题
6 . 如图,在五面体
中,底面
的对角线
交于点
,
为等边三角形,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540d0fba5d871492b8956f39cc96fea4.png)
.
(1)证明:
平面
;
(2)若五面体的体积为
,当直线
与直线
所成的角最大时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dea53cfe562dc39821a67aec2a9ec98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540d0fba5d871492b8956f39cc96fea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/625d61af-898b-46a2-b1ca-c6a2cc525725.png?resizew=126)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若五面体的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ac1cafa010bf62459ecc36a1a23fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306681bd5aaa51e9c63ab3002e23dec5.png)
您最近一年使用:0次
解题方法
7 . 如图,在三棱台
中,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/137aace9-2c25-4ea0-89e3-97c7b041cacc.png?resizew=168)
(1)求证:面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
平面
;
(2)求面
与面
所成二面角正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec7357e3cd98a0815c1cdf2c7441ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/137aace9-2c25-4ea0-89e3-97c7b041cacc.png?resizew=168)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在四棱锥
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
,
,
,
,
分别为棱
,
的中点
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/809fa2ed-94e7-443c-9231-61441f30e5f4.png?resizew=147)
(1)求证:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
平面
;
(2)求平面
与平面
所成二面角的正弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103d11f633c98ea13f503802a54fe1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d536d472718bfec67184aaa45af29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/809fa2ed-94e7-443c-9231-61441f30e5f4.png?resizew=147)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2024-02-03更新
|
252次组卷
|
3卷引用:【名校面对面】2022-2023学年高三大联考(5月) 理数试题
9 . 如图所示,在四棱锥
中,
,
,点
为线段
的中点,且
.
(1)![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/79589905-ba6e-4620-96cc-0de9a2b31377.png?resizew=185)
求证:
;
(2)已知点
为线段
的中点,点
在线段
上(不含端点位置),若直线
与平面
所成的角的正切值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57af480a5e2c688723d762b822fa51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8482b9583a2fd67a1a990935119c4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0c8e20e8d0931eb58b199a5e808d72d.png)
(1)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/79589905-ba6e-4620-96cc-0de9a2b31377.png?resizew=185)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e307ad6d6960b18a872c448c00aa30d.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c157ff302a881c17514534903c575f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585a36dc7fe184aa99338bb2ecf1b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c46496c760e808d219459f55ca511d.png)
您最近一年使用:0次
2023-12-30更新
|
289次组卷
|
2卷引用:华大新高考联盟2024届高三上学期11月教学质量测评(新教材卷)数学试题
名校
解题方法
10 . 在直三棱柱
中,
分別为
的中点,
.
(1)证明:
平面
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0ed802b75a87199155189b401a5c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea60422877be74518dcf42d80953099a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/e251e37d-1c71-4db0-84ec-a353fbc9d039.png?resizew=186)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ae72f5e5891249caa10c43224da89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431e8bf1a5f9ac9a2ec82c11f31a4afe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd91784222c2814ce7158c39c830a8b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace8e069c60eb35e5d6d66ab9f16cf11.png)
您最近一年使用:0次
2023-12-29更新
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223次组卷
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2卷引用:2024届高三上学期一轮复习联考(四)数学试题